the reach of direct numerical simulation—that is, through a solution of the equations of motion with no approximations—for the foreseeable future. The difficulty arises from the combination of the large required spatial and temporal dynamic range and from the three-dimensional dynamics. Considerable insights can, however, be gleaned from simulations that advance the envelope in this fashion, exploiting increases in computational power with simulations relying on the fewest approximations possible. High energy density simulation codes include advection algorithms for the simulation of shocks and also vortical- and magnetic-field-driven instabilities, equation-of-state models that extend from solid to plasma regimes, and detailed electron and radiation transport and opacity packages that can provide an adequate estimate of the energy transport for the full range of high energy density temperatures and densities. Furthermore, some of these codes model the intense electromagnetic wave/particle interaction of high-intensity beams, from plasma coronal nascence through high-density heating. While no codes include all of these effects simultaneously, relevant parts of high energy density physics problems can be simulated, yielding results with predictive value. Such simulations advance our understanding of complex phenomena, yield insights that are fundamental in interpreting and designing experiments, and provide data for new theories and models.

Hardware and computation algorithm advances are required in order to continue to address these problems. Given a span of phenomena in a typical high energy density problem, simulations become tractable as more physics is modeled rather than simulated at every point in space and time. While in a way this is always the case—we rely on continuum and other approximations to simulate hydrodynamics—the complexity of high energy density problems requires an increase in the level of modeling and abstraction. Physics-based subgrid-scale and other phenomenological models that permit a reduction in the number of grid points on which the dynamics must be solved can potentially achieve this. Such models will rely on theoretical advances and special, well-characterized experiments that probe dynamics at small scales and validate the simulations that have incorporated the subgrid-scale models.

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